Search results for "equation"
showing 10 items of 4219 documents
The Two Loop Crossed Ladder Vertex Diagram with Two Massive Exchanges
2008
We compute the (three) master integrals for the crossed ladder diagram with two exchanged quanta of equal mass. The differential equations obeyed by the master integrals are used to generate power series expansions centered around all the singular (plus some regular) points, which are then matched numerically with high accuracy. The expansions allow a fast and precise numerical calculation of the three master integrals (better than 15 digits with less than 30 terms in the whole real axis). A conspicuous relation with the equal-mass sunrise in two dimensions is found. Comparison with a previous large momentum expansion is made finding complete agreement.
A Perturbation Approach to Continuous-Time Portfolio Selection Under Stochastic Investment Opportunities
2013
This paper studies portfolio selection in continuous-time models with stochastic investment opportunities. We consider asset allocation problems where preferences are specified as power utility derived from terminal wealth as well as consumption-savings problems with recursive utility Epstein-Zin preferences. The paper approximates the associated dynamic programming problem by perturbing the coefficients of the stochastic dynamics. We represent the Hamilton-Jacobi-Bellman equation as a series of partial differential equations that can be solved iteratively in closed-form through computer algebra software, at any desired accuracy.
The inviscid limit and Prandtl's asymptotic expansion for incompressible flows in the half space
2022
The validity of the inviscid limit for the incompressible Navier-Stokes equations is one of the most important and challenging problems in the mathematical theory of fluid dynamics: the motion of inviscid fluids is described by the Euler equations, so, when the viscosity goes to zero, one would expect the convergence of NS solutions to the Euler solutions. However, NS equations are a singular perturbation of the Euler equations: the change of order of the equation implies that fewer boundary conditions can be imposed on the inviscid flows. Therefore, the no-slip boundary conditions, imposed on the NS solutions, are not satisfied by the Euler flow, for which a tangential slip is allowed. Thi…
Analysis of complex singularities in high-Reynolds-number Navier-Stokes solutions
2013
AbstractNumerical solutions of the laminar Prandtl boundary-layer and Navier–Stokes equations are considered for the case of the two-dimensional uniform flow past an impulsively-started circular cylinder. The various viscous–inviscid interactions that occur during the unsteady separation process are investigated by applying complex singularity analysis to the wall shear and streamwise velocity component of the two solutions. This is carried out using two different methodologies, namely a singularity-tracking method and the Padé approximation. It is shown how the van Dommelen and Shen singularity that occurs in solutions of the Prandtl boundary-layer equations evolves in the complex plane be…
Singularity formation and separation phenomena in boundary layer theory
2009
In this paper we review some results concerning the behaviour of the incompressible Navier–Stokes solutions in the zero viscosity limit. Most of the emphasis is put on the phenomena occurring in the boundary layer created when the no-slip condition is imposed. Numerical simulations are used to explore the limits of the theory. We also consider the case of 2D vortex layers, i.e. flows with internal layers in the form of a rapid variation, across a curve, of the tangential velocity.
Singularities for Prandtl's equations.
2006
We used a mixed spectral/finite-difference numerical method to investigate the possibility of a finite time blow-up of the solutions of Prandtl's equations for the case of the impulsively started cylinder. Our toll is the complex singularity tracking method. We show that a cubic root singularity seems to develop, in a time that can be made arbitrarily short, from a class of data uniformely bounded in H^1.
Measuring perceived community support: Factorial structure, longitudinal invariance, and predictive validity of the PCSQ (perceived community support…
2007
Social support from intimate and confiding relationships has received a great deal of attention; however, the study of the community as a relevant source of support has been comparatively lacking. In this article, we present a multidimensional measure of community support (Perceived Community Support Questionnaire, PCSQ). Through exploratory and confirmatory factor analyses on data from three samples of adult population (two-wave panel: sample 1, N = 1009 and sample 2, N = 780; and an independent sample 3, N = 440), results show that community integration, community participation, and use of community organizations are reliable indicators of the underlying construct of perceived community s…
Trait self-control and self-discipline : Structure, validity, and invariance across national groups
2021
The aim of the present study was to test the validity of the Brief Self-Control Scale (BSCS; Tangney, Baumeister and Boone 2004) including its dimensional structure based on competing one- and two-factor models, discriminant validity from the conceptually-related self-discipline construct, invariance across multiple samples from different national groups, and predictive validity with respect to health-related behaviors. Samples of undergraduate students (total N = 1282) from four national groups completed the brief self-control scale, the self-discipline scale from the NEO-PI-R, and self-report measures of binge drinking, exercise, and healthy eating. Confirmatory factor analytic models sup…
Comparison of parallel implementation of some multi-level Schwarz methods for singularly perturbed parabolic problems
1999
Abstract Parallel multi-level algorithms combining a time discretization and an overlapping domain decomposition technique are applied to the numerical solution of singularly perturbed parabolic problems. Two methods based on the Schwarz alternating procedure are considered: a two-level method with auxiliary “correcting” subproblems as well as a three-level method with auxiliary “predicting” and “correcting” subproblems. Moreover, modifications of the methods using time extrapolation on subdomain interfaces are investigated. The emphasis is given to the description of the algorithms as well as their computer realization on a distributed memory multiprocessor computer. Numerical experiments …
Numerical prediction of turbulent flow and heat transfer in helically coiled pipes
2010
Abstract Computational results were obtained for turbulent flow and heat transfer in curved pipes, representative of helically coiled heat exchangers. Following a grid refinement study, grid independent predictions from alternative turbulence models ( k – ɛ , SST k – ω and RSM– ω ) were compared with DNS results and experimental pressure drop and heat transfer data. Using the SST k – ω and RSM– ω models, pressure drop results were in excellent agreement with literature data and the Ito correlation. For heat transfer, the literature is not comparably complete or accurate, but a satisfactory agreement was obtained in the range of available data. Unsatisfactory results, both for pressure drop …